RJ.Berger wrote:If x > 1, what is the value of integer x?
(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.
I know that only A is true and B is not sufficient but I did not understand why A is sufficient. Maybe I did not get the first statement right. What does "there are x unique factors of x" exactly mean?
Thank you in advance.
Statement 1: There are x unique factors of x.
The only value that works here is x=2: 2 has two unique factors (1 and 2), so the number of unique factors (2) is equal to x (2).
No other value works.
To illustrate:
If x=10, x will have 4 distinct factors (1,2,5,10), so the number of unique factors (4) is not equal to x (10).
If x=16, x will have 5 unique factors (1,2,4,8,16), so the number of unique factors (5) is not equal to x (16).
Thus, x=2.
SUFFICIENT.
Statement 2: The sum of x and any prime number larger than x is odd.
Any prime number greater than 2 is odd.
It's possible that x=2, since 2+odd = odd.
It's possible that x=4, since 4+odd = odd.
INSUFFICIENT.
The correct answer is
A.
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